Size bias, sampling, the waiting time paradox, and infinite divisibility: when is the increment independent?
msra(2010)
摘要
With $X^*$ denoting a random variable with the $X$-size bias distribution,
what are all distributions for $X$ such that it is possible to have $X^*=X+Y$,
$Y\geq 0$, with $X$ and $Y$ {\em independent}? We give the answer, due to
Steutel \cite{steutel}, and also discuss the relations of size biasing to the
waiting time paradox, renewal theory, sampling, tightness and uniform
integrability, compound Poisson distributions, infinite divisibility, and the
lognormal distributions.
更多查看译文
关键词
lognormal distribution,random variable,compound poisson distribution,infinite divisibility,renewal theory
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要